Time synchronization is a long-standing challenge in distributed systems like indoor/outdoor positioning, coordinated multi-point in 4G/5G mobile communication, etc., which require nanosecond-level high-reliable time sync networks. At present, a widely adopted solution for time sync networks is the precision time protocol specified in IEEE 1588v2, which can provide sub-microsecond sync accuracy. In addition, a novel network time sync method called distributed time synchronization has also been proposed recently, which can achieve 50-ns-level accuracy and stronger survivability in metro, regional, and backbone networks. However, both of the above methods encounter difficulties in achieving nanosecond sync accuracy and network reliability simultaneously. In this paper, by analyzing the main factors influencing the degradation of time sync accuracy, we reveal that the finite clock resolution is a major barrier to achieving nanosecond-level time synchronization. In order to establish a low-cost, high-reliability, and sub-nanosecond-level time sync network, we propose a novel network time sync method called double-frequency distributed time synchronization (DF- DTS). By selecting two specific and distinct frequencies for the sending and receiving clocks of the nodes/devices being synchronized, the time sync errors induced by the finite clock resolution can be reduced by a statistical approach. We set up a theoretical model for the DF-DTS and analyze the time sync accuracy through both mathematical derivations and network simulations. Furthermore, we propose a failure-restoration mechanism to enhance the reliability of DF-DTS networks by improving the time sync accuracy under failures and reducing the failure recovery time. Finally, we conduct both point- to-point and network time sync experiments to validate the proposed DF-DTS method. The results demonstrate that DF-DTS can achieve sub-nanosecond-level sync accuracy that is 1-2 orders of magnitude higher than the clock resolution in a prototype four-node DF-DTS network. Moreover, a network simulation under failure cases is conducted, and the results show that our method has significant advantages in both time sync accuracy and recovery time in the failure-restoration process compared to IEEE 1588v2.